Sentence examples for i of degree from inspiring English sources

By induction on degree, it suffices to show that for any object (i in I) of degree (n = deg (i)), a splitting map q over (I_{le n-1}) can be extended to i.

Moreover, let (overline{M(I)}_n = rho ^{-1} overline{I}_n) subset M(I_{le n}) subset M(I)) be the union of the fibers (M(I)_i) of the prefibration (rho :M(I) rightarrow I) over all objects (i in I) of degree (deg (i)=n), and denote by (varepsilon _n:overline{M(I)}_n subset M(I_{le n})) the embedding functors.

An equivalent way of giving a good filtration is to give a "degree function" (deg ) that associates a non-negative integer n to any object (i in I), so that (I_{le n}) is the full subcategory spanned by objects i of degree (deg (i) le n).

Consider an even Majorana monomial s 1 : = L ( ∏ i ∈ I m i ) of degree 2 d ′, where s 2 is defined using the ordered index set ℐ, and a quadratic operator s 2 : = L ( m p m q ) with p ∈ I and q ∉ I.

This could be efficiently done in O(1) time for each pair of neighbors by checking their corresponding entry in the adjacency matrix, leading to a time complexity of O k_{i}^{2})) for a vertex i of degree (k_{i}).

The scheme with the Bassi-Rebay flux is stable for the polynomial interpolation of shape functions ϕ i of degree higher then 1.

The analytic form of the Laguerre polynomials L i (x) of degree i is given as follows: L i ( x ) = ∑ k = 0 i ( − 1 ) k i ! ( i − k ) ! ( k ! ) 2 x k, Open image in new window (14).

Proof Using the analytic form of the modified generalized Laguerre polynomials L i ( x ) of degree i (6) and (2), then J ν L i ( x ) = ∑ k = 0 i ( − 1 ) k β k Γ ( i + α + 1 ) ( i − k ) ! k !

Proof The analytic form of the MGLP L i ( x ) of degree i is obtained by (7).

Choose random non-zero polynomials c i j (t) of degree d i j for ((i,j) in Lambda ^{(p)} smallsetminus { (0, 0) }).   3.

Now assume given an object (i in I) of some degree (n = deg (i)).